(Neil may be sorry he asked). -Sum[(z^k*(2*k*z + 2*a*z + z + 2*k^2 + 4*a*k + 5*k + 2*a^2 + 5*a + 3))/ ((2*k + 2*a + 1)*(2*k + 2*a + 3)*(k + a)!), {k, 0, Infinity}] ==((Gamma[a, z]/Gamma[a] - 1)*E^z)/z^a + 1/((2*a + 1)*Gamma[a]) It's easy to take the confluent limit of the Rosetta 3by3 system, but then it's unclear how to specialize to triangularize the non pFp matrices. Maybe continued fractions would be a better target. --rwg